Vortex Processes and Solid Body Dynamics The Dynamic Problems of Spacecrafts and Magnetic Levitation Systems

Vortex Processes and Solid Body Dynamics The Dynamic Problems of Spacecrafts and Magnetic Levitation Systems / by B. Rabinovich, A.I. Lebedev, A.I. Mytarev.

... a wise man knows all things in a manner in which this is possible, not, however, knowing them individually. Aristotle. Metaphysics * The problem of consideration of vortex fields' influence on solid body dynamics has a long history. One constantly comes upon it in flight dynamics of airplan...

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Bibliographic Details
Main Authors: Rabinovich, B. (Author), Lebedev, A.I (Author), Mytarev, A.I (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Dordrecht : Springer Netherlands : Imprint: Springer, 1994.
Edition:1st ed. 1994.
Series:Fluid Mechanics and Its Applications, 25
Springer eBook Collection.
Subjects:
Automotive engineering.
Electrical engineering.
Vibration.
Dynamical systems.
Dynamics.
Mechanics.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 1. Mathematical Models of Electrical Conductivity Ferromagnetic Elements with Eddy Currents
  • 1.1. Statements of the Problem
  • 1.2. Asymptotic Solution of Unsteady Boundary-Value Problems for Magnetic and Electrical Fields
  • 1.3. Eddy Currents Mathematical Model
  • 1.4. General Equations of System Dynamics with External and Eddy Currents and Mechanical Degrees of Freedom
  • 1.5. Mathematical Models of Stabilized Ferromagnetic Elements as Objects of Control
  • 1.6. Mathematical Models of the Electromagnetic Levitation System Actuator
  • 2. Mathematical Models of Stabilazed Objects with Compartments Containing Vortex Low-Viscous Liquid
  • 2.1. Mathematical Models of a Solid Body with Cavity Partially Filled with Ideal Liquid
  • 2.2. Velocity Field of LV Liquid Vortex Motion in a Moving Cavity
  • 2.3. Generalized Forces and Derivatives of Liquid Kinetic Energy with Respect to Generalized Velocities
  • 2.4. The Mathematical Model of a Solid Body with a Cavity Containing Vortex Low-Viscous Liquid
  • 2.5. Axially Symmetric Body. Particular Cases of General Equations of Perturbed Motion
  • 2.6. Axisymmetric Body. Coefficients Conversion Formulae
  • 2.7. Axisymmetric Body. Derivation of Equations of the Body — Liquid System Perturbed Motion from the Variational Principle
  • 2.8. Spacecraft with LPRE Stabilized Attitude
  • 2.9. Spacecraft with LPRE, Slowly Rotating around Its Longitudial Axis
  • 2.10. Determination of Hydrodynamic Coefficients
  • 3. Analytical and Numerical Methods of Dynamics Investigation of Vehicles Described by Vortex Models
  • 3.1. Preliminary Remarcs
  • 3.2. Analytical Methods of Investigation. Harmonic Balance Method
  • 3.3. An Algorithm for Numerical Solution of a Set of Integrodifferential Equations with a Singular Kernel of the Type (t ? ?)??2
  • 3.4. Methodological Example
  • 4. Experimental Verification of Mathematical Models for Eddy Currents and Vortex Motions of Liquid
  • 4.1. Mathematical Models Used for Experimental Data Processing
  • 4.2. Determination of Mathematical Model Parameters Based on Experimental Results
  • 4.3. Scheme of the Experiment and Primary Processing of Results
  • 4.4. Verification of Models for Eddy Currents in HECF Elements
  • 4.5. Low-Viscous Liquid Vortex Motions Model Verification
  • 5. Some Dynamics Problems for Systems with Electromagnetic Actuators
  • 5.1. Characteristic Properties of Electromagnet as an Object of Control. Requirements to the Air Gap Regulation System
  • 5.2. Mathematical Model of the Two-Mass System ’Controlled Electromagnet — Mass with Elasto-Viscous Suspension’
  • 5.3. Measurements Composition Influence on Required Completeness of Controlled Electromagnet Mathematical Model
  • 5.4. Eddy Currents Influence on Closed-Loop System Dynamics. Reduction of Integrodifferential Equations to an Equivalent Set of Differential Equations
  • 6. Some Dynamics Problems for a Spacecrafts Having Compartments Partially Filled with Liquid
  • 6.1. Stabilizability and Dynamic Stability of Spacecrafts Having Compartments Partially Filled with Liquid
  • 6.2. Simplified Mathematical Models of Perturbed Motion for a Spacecraft Having Compartments Partially Filled with Liquid
  • 6.3. Self-Sustained Oscillations in the Closed-Loop System ’Spacecraft — Liquid — Controller’
  • 6.4. SC Stability in the Yaw Plane with Account of Potential and Vortex Motions of Liquid in Tanks
  • 6.5. SC Stability in the Roll Plane for Non-Small Amplitudes of Angular Oscillations
  • 7. Examples of Control Law Synthesis for an Object Described by a Vortex Model
  • 7.1. A Control Law Allowing Hardware Implementation, Based on Air Gap Sensor and Current Transducer Indications
  • 7.2. Synthesis of a Relay-Controller Closed-Loop System
  • 7.3. Mathematical Modelling of Electromagnetic Levitation System Dynamics
  • 8. Some Dynamics Problems for a Solid Body with Electrically Conductive Liquid Moving in Magnetic Field
  • 8.1. Statements of the Problem. Main Assumptions
  • 8.2. Magnetic Hydrodynamics Boundary-Value Problems for LVECF Liquid
  • 8.3. Liquid — Magnetic Field System Kinetic Energy. Generalized Forces and Generalized Voltages
  • 8.4. Equations of Dynamics for a Solid Body Containing LVECF Liquid with Related Magnetic Field Presence
  • 8.5. Equations of Dynamics for a Solid Body with a Cavity of Revolution Having Narrow Internal Ribs
  • 8.6. The Case of a Circular Cylinder-Shaped Cavity
  • 8.7. Magnetic Field Influence on Solid Body — LVEC Liquid Open-Loop System Frequency Response
  • 8.8. The Possibility of Using Magnetohydrodynamic Effects to Ensure Dynamic Stability of Spacecraft
  • Conclusion.

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